This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to a particular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and \(N\)-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random and Ergodic Schrödinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. Exhaustive lists of references enhance the presentation offered in these surveys.

A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensive introduction into an area covered in this volume.

Readership

Research mathematicians interested in mathematical physics and spectral theory.

Reviews

"Both nicely edited volumes sum almost 1000 pages of interesting surveys and exhaustive bibliography that clearly benefits graduate students and researchers seeking for a quick introduction into areas mentioned above. Even if you are interested only in the topics covered in Part II, don't miss 'A selection of Barry stories' at the beginning of Volume I. After having a chance to collaborate with Barry, I felt totally identified with the stories, mostly humorous, but reflecting Simon's energy, passion and style of work."